Worldbuilding For Writers Number Two: Finding The Habitable Zone

In this installment of Worldbuilding for Writers, Gamers and Other Creatives, we're going to determine the habitable zone for the planet you're building for your storyworld. It's going to take us a few steps to get there, and yes, there is some math, but it's nothing your calculator or spreadsheet software can't handle. Hang in there!

What Is The Habitable Zone

In brief, the habitable zone is the minimum and maximum distance a planet should orbit its star in order to be most hospitable for life as we know it. For our purposes, it's the orbital distance from the star that will permit an Earth-like planet. In particular, the planet should receive enough heat energy from its star to allow for the presence of liquid water. The opinions of astronomers vary on just what this "Goldilocks zone" should be for any given star, but many agree that the habitable zone of Sol is between 0.725 to 1.24 astronomical units from the Sun — that is, about three-quarters to one and a quarter times the distance of the Earth from the Sun.

Understand that this is an estimation drawn from science-based extrapolation. There are many, many factors that go into what makes a world suitable for life (some of which we'll get into in later installments of Worldbuilding for Writers) but for the purposes of building our worlds, we're going to go with this range and play with it.

Gathering Data

Given the acceptance of a range of distances determining the habitable zone around Sol, we can determine the habitable zones of other stars. Since it all comes down the the amount of heat received from the star at a given distance, we need to know a little bit more about the star our world orbits.

Mass and Luminosity

Specifically, we need to determine the star's luminosity and temperature. For stars between F5 and K5 on the main sequence, we can determine both from the star's mass. Here are approximate masses (relative to Sol) for our eligible stars:

Spectral Class
Mass
Spectral Class
Mass
Spectral Class
Mass


F5
1.201
G2
1.000
G9
0.810


F6
1.161
G3
0.973
K0
0.790


F7
1.121
G4
0.946
K1
0.752


F8
1.081
G5
0.919
K2
0.714


F9
1.041
G6
0.891
K3
0.677


G0
1.039
G7
0.864
K4
0.639


G1
1.020
G8
0.837
K5
0.601

From this, we can determine the luminosity of the star by taking the mass and raising it to the 3.5 power. If you recall, the Shaper's World's star, Tah, is a G3 star, which gives it a mass of .973.

.973^3.5 = .9086

So Tah, the star of the Shaper's World, has a luminosity of .9086 relative to Sol.

Finding the Habitable Zone

Now that we have the star's luminosity and know the suggested upper (closest to the star) and lower (farthest from the star) limits of the habitable zone, we can find the range of the habitable zone in astronomical units (AU) within which our planet must orbit to have a chance at being Earth-like. Here's how it works:

Inner Limit

The inner limit of the habitable zone of our own solar system is suggested to be 0.725 AU. At that point in space, a planet would receive 1.9 times the energy (or insolation) received by the Earth. We figure that out by dividing luminosity by the distance of the planet squared, or

1 / .725^2 = 1.9024

We can turn that around to see how the insolation can reveal the distance by dividing the luminosity by the insolation and taking the square root of the result:

1 / 1.9024 = 0.5256. The square root of 0.5256 = 0.725

Given that, we can now determine the inner limit of the habitable zone of Tah, the star of the Shaper's World. Remember that Tah is a G3 star with a luminosity of .9086.

0.9086 / 1.9024 = 0.4776. The square root of 0.4776 = 0.6911

The inner limit of Tah's habitable zone is 0.6911 AU.

The Outer Limit

For the outer limit, we figure the insolation at the maximum suggested distance for Sol's habitable zone, which is 0.6503:

1 / 1.24^2 = 0.6503

From that, we can see that the outer limit of the habitable zone of Tah is 1.1820 AU:

0.9086 / 0.6503 = 1.3972. The square root of 1.3972 = 1.1820

The Earth Twin Distance

Let's say you want to determine the distance a planet needs to be from your star in order receive the same amount of energy the Earth receives from Sol. This is an easy one — take the square root of your star's luminosity and you have the distance in AU!

For the Shaper's World, the Earth Twin distance is 0.9532 AU.

Wrapping It Up

The habitable zone of Sol is between .725 and 1.24 astronomical units from the sun, with the Earth sitting pretty at 1 AU. The habitable zone of the Shaper's World is between 0.6911 and 1.1820 astronomical units from Tah, with the "Earth Twin" distance — the distance where the Shaper's World would receive the same energy the Earth does from Sol — at 0.9532 AU. What is the habitable zone of your world? Tell us in the comments!

Next

Now that we know the habitable zone for our star, we can play around with orbital distances for our planet, which will help determine the length of the year and the base temperature… next week!

Matthew Wayne Selznick - Telling stories with words, music, pictures and people.